Consider a curve of genus one over a field K in one of three explicit forms: a double cover of P 1 , a plane cubic, or a space quartic. For each form, a certain syzygy from classical invariant theory gives the curve's jacobian in Weierstrass form and the covering map to its jacobian induced by the K
Curves of genusglying on ag-dimensional Jacobian variety
โ Scribed by Fabio Bardelli; Gian Pietro Pirola
- Publisher
- Springer-Verlag
- Year
- 1989
- Tongue
- English
- Weight
- 632 KB
- Volume
- 95
- Category
- Article
- ISSN
- 0020-9910
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๐ SIMILAR VOLUMES
## Abstract In this paper a system of coordinates for the effective divisors on the Jacobian Variety of a Picard curve is presented. These coordinates possess a nice geometric interpretation and provide us with an unifying environment to obtain an explicit structure of algebraic variety on the Jaco
In this paper we confine ourselves to the study of the JAcoBran variety J(C) of a PICARD curve C defined over a field K of characteristic p > 0, with the aim to obtain explicit conditions under which the JACOBIan variety is ordinary or supersingular, in terms of the HASSE-WITT matrix of the PICARD c
We confirm a conjecture of L. Merel (H. Darmon and L. Merel, J. Reine Angew. Math. 490 (1997), 81-100) describing a certain relation between the jacobians of various quotients of X p in terms of specific correspondences. The method of proof involves reducing this conjecture to a question about certa
Let \(J\) be the Jacobian of the hyperelliptic curve \(Y^{2}=f\left(X^{2}\right)\) over a field \(K\) of characteristic 0 , where \(f\) has odd degree. We shall present an embedding of the group \(J(K) / 2 J(K)\) into the group \(L^{* / L^{* 2}}\) where \(L=K[T] / f(T)\). Since this embedding is der